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Some results on Newton equation with an additional stochastic force

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Stochastic Differential Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 126))

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Abstract

In this report, based on joint work with E. Zehnder, we discuss stochastic perturbations of classical Hamiltonian systems by a white noise force. We give existence and uniqueness results for the solutions of the equation of motion, allowing for forces growing stronger than linearly at infinity. We prove that Lebesgue measure in phase space is a σ-finite invariant measure. Moreover we give a Girsanov formula relating the solutions for a nonlinear force to those for a linear force.

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Author information

Authors and Affiliations

  1. Fakultät für Mathematik, Ruhr-Universität-Bochum, FRG

    S. Albeverio

  2. BiBoS-Research Centre, SFB 237 Bochum-Essen-Düsseldorf, Germany

    S. Albeverio

  3. CERFIM Locarno (CH), Switzerland

    A. Hilbert

Authors
  1. S. Albeverio
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  2. A. Hilbert
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Editor information

Norbert Christopeit Kurt Helmes Michael Kohlmann

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© 1989 Springer-Verlag

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Albeverio, S., Hilbert, A. (1989). Some results on Newton equation with an additional stochastic force. In: Christopeit, N., Helmes, K., Kohlmann, M. (eds) Stochastic Differential Systems. Lecture Notes in Control and Information Sciences, vol 126. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0043768

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  • DOI: https://doi.org/10.1007/BFb0043768

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51299-8

  • Online ISBN: 978-3-540-46188-3

  • eBook Packages: Springer Book Archive

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